This is more a discussion of economics than language, but here goes.
There are three different numbers to be considered here, in the context of your question and the article you reference: gross savings as percent of income, net savings as percent of income, and savings rate.
Suppose you make $50,000 per year and every year you save $5,000. Then your "savings rate" is 10%.
But after a few years you will have much more than $5,000 in the bank. Suppose that at some point -- whether this is all money that you deposited or if you collected some interest, made profits on investments, whatever -- suppose you now have $30,000 in the bank. Then your "gross savings as percent of income" is 30,000 / 50,000 = 60%.
But you might also have debts. Suppose you have $10,000 in debts. In that case, your net savings are 30,000 - 10,000 = 20,000, and thus your "net savings as percent of income" are 20,000 / 50,000 = 40%.
Normally if someone says "savings" they mean "gross savings". Like, if you asked the bank teller, "How much so I have in my savings account?", they would tell you the gross balance in the account, they wouldn't subtract any debts.
Also, normally "savings" is understood to include just liquid assets, that is, cash plus things like stocks and bonds that can be turned into cash at a predicatable value within a few days. You don't normally include the value of your house or your car or the market value of that new invention you're working on as "savings". These things WOULD be included as part of "net worth". (Well, the house and car anyway.)
Of course this makes a huge difference. If you say, "I have $500,000 in the bank!" that sounds great. But if it turns out that you also bought a house during the housing boom that you still owe $600,000 on even though now it is worth only $100,000, that changes your financial picture considerably. Or if you say, "I have only $20 in the bank", that sounds pretty depressing. But if a big energy company has just told you that they discovered oil in your back yard and they're prepared to sign a contract promising you a million dollars a year for twenty years if you let them drill, that might make a difference to your future. On the other hand, if that million a year won't start for ten years, that isn't much help in paying the electric bill today. So a statistic can be completely true but also very misleading. You have to know exactly what is being counted, and why we want to know.
I don't have a copy of Gingrich's original speech, all I know is what they quoted in that article you referenced. So I can't comment on how he described the statistic. But the statement they quote, "they have 72 percent of the GDP in savings", is correct. It looks to me like he even carefully worded it to avoid ambiguity: he didn't say "they save 72% of their income" which could sound like he meant they save 72% every year, rather than that they've accumulated a total of 72% of one-year's income.
The article itself says that a few years ago they said it was 65%. It is not unreasonable to suppose that it might have gone up a few percentage points in two years. And numbers like this are hard to calculate precisely: how do you track down every bank account in the country, exactly what types of accounts and what kind of assets are included, etc, etc.? For that matter, who says their 65% is correct? Where did they get their number? If there's a discrepancy, maybe Gingrich's number is right and their's is wrong. In any case, I don't think the debate here is about whether the exact number is 65 or 72 or 68, but rather whether it's a lot or a little.
So from the information available, I'd say that Gingrich's statement is absolutely true. Maybe if I read the whole speech it would become apparent that he's quoting an accurate statistic and then describing it in a false or misleading way, or that he's making a true statement and then drawing unwarranted conclusions from it. Without seeing the text of the speech, I can't say.
I don't know whether this web site that your referencing is run by people who agree or disagree with Mr Gingrich or who are truly trying to be fair. I'm always cautious about anyone who claims to be an unbiased aribter of controversial social or political questions. Maybe they're really unbiased and maybe they're not.
In reply to your follow-up question: As I understand the article, they aren't saying that Gingrich confused accumulated savings with savings rate, but that he confused gross savings with net savings. The writers themselves seemed confused about what the term "savings rate" means, as they appeared to use it interchangeably with "net accumulated savings", which is not the same thing at all.
But they only quote one sentence from Gingrich and that sentence is, in fact, accurate. Perhaps Mr Gingrich made other statements that really were inaccurate. But the article doesn't quote them or even summarize them. Their only evidence is to quote someone else as saying that Gingrich's words were "phrased badly".
Frankly, that makes me suspicious of the fairness or competence of the writers of this article. They say that Mr Gingrinch made inaccurate statements. But they don't tell us what those inaccurate statements were. They presume to be judges of the accuracy of what others say, but they offer zero real evidence to back up their own statements.